RATIONALE: Giving low doses of chemotherapy and total-body irradiation before a donor umbilical cord blood stem cell transplant helps stop the growth of cancer or abnormal cells. It also stops the patient's immune system from rejecting the donor's stem cells. The donated stem cells may replace the patient's immune cells and help destroy any remaining cancer or abnormal cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving tacrolimus and mycophenolate mofetil before the transplant may stop this from happening.

PURPOSE: This clinical trial is studying how well umbilical cord blood stem cell transplant works in treating patients with hematologic cancer or other disease.

OBJECTIVES:

Primary

• Determine the efficacy of double umbilical cord blood stem cell transplantation using a conditioning regimen comprising lower doses of busulfan and fludarabine phosphate and low-dose total body irradiation, in terms of stem cell engraftment at 60 days post transplantation, in patients with hematologic cancer or other diseases.
• Determine the merits of conducting a larger, comparative study of this regimen.

Secondary

• Determine mortality within 100 days of transplantation in these patients.

OUTLINE: This is a pilot study.

• Reduced-intensity conditioning regimen: Patients receive busulfan IV over 3 hours on days -9 to -8 and fludarabine phosphate IV on days -7 to -3. Patients then undergo low-dose total body irradiation on day 0.
• Graft-versus-host disease prophylaxis: Patients receive tacrolimus IV twice daily and mycophenolate orally or IV three times daily beginning on day -3.
• CNS prophylaxis and/or treatment: Patients with a history of CNS involvement receive prophylactic cytarabine (Ara-C) intrathecally (IT) prior to transplant. Patients also undergo lumbar puncture (LP) to test for active CNS disease. Patients with cerebrospinal fluid positive for leukemia receive Ara-C IT every 2-3 days until a repeat LP shows no remaining leukemic cells. Three days after the last LP and after one final dose of Ara-C, patients begin the conditioning regimen.
• Double umbilical cord blood (UCB) donor stem cell transplantation (SCT): Patients undergo double UCB donor SCT on day 0.

PROJECTED ACCRUAL: A total of 30 patients will be accrued for this study.

DISEASE CHARACTERISTICS:

• Histologically confirmed diagnosis of 1 of the following:

  • Acute myeloid leukemia meeting the following criteria:

    • M0-M7 histologic subtypes by French-American-British classification

    • Previously treated disease

    • Meets 1 of the following criteria:

      • Persistent disease as evidenced by 5-30% persistent blasts in bone marrow after induction or salvage therapy

      • In second or subsequent complete remission (CR)

      • In first CR with 1 of the following high-risk features:

        • Philadelphia chromosome present
        • Noncore-binding factor type of chromosomal abnormalities

  • Myelodysplastic syndromes with 1 of the following International Prognostic Scoring System (IPSS) scores:

    • Intermediate-1
    • Intermediate-2
    • High-risk score with transfusion dependence

  • Chronic myelogenous leukemia meeting 1 of the following criteria:

    • In accelerated or blastic phase
    • Failed prior imatinib mesylate therapy

  • Acute lymphoblastic leukemia meeting 1 of the following criteria:

    • In first CR with any of the following high-risk features:

      • Philadelphia chromosome present
      • Translocation t(4;11) present
      • WBC > 30,000/mm³ (adult patients)
      • More than 4 weeks from initiation of treatment was required to achieve CR (adult patients)
      • DNA index of near haploid (N=23 chromosomes) (pediatric patients)

    • In second or subsequent CR

    • Persistent disease as evidenced by 5-20% persistent blasts in bone marrow after induction or salvage therapy

  • Hodgkin's or non-Hodgkin's lymphoma meeting the following criteria:

    • Recurrent or refractory disease
    • Tumor ≤ 5 cm in diameter

  • Myeloma or plasma cell neoplasm meeting 1 of the following staging criteria:

    • Stage III at presentation

    • Stage I-II at presentation

      • Not responding OR progressed after first-line therapy

  • Chronic lymphocytic leukemia or Waldenstrom's macroglobulinemia with refractory or progressive disease after first-line therapy

• No 5-6/6 HLA-matched related or 7-8/8 HLA-matched unrelated marrow or peripheral blood stem cell donor available

• No single 4-6/6 HLA-A, -B, or -DRB1-matched umbilical cord blood unit ≥ 3.5 x 10^7 nucleated cells/kg available

PATIENT CHARACTERISTICS:

• ECOG performance status (PS) 0-2 OR Karnofsky or Lansky PS 70-100%
• Not pregnant
• Fertile patients must use effective contraception prior to and during study participation
• HIV negative
• Bilirubin < 3.0 mg/dL
• AST and ALT ≤ 3 times upper limit of normal
• Creatinine < 2.0 mg/dL OR creatinine clearance > 50 mL/min
• Cardiac ejection fraction > 50% by echocardiogram OR shortening fraction > 27%
• No uncontrolled symptomatic congestive heart failure
• No unstable angina pectoris
• No cardiac arrhythmia
• FEV_1 > 50% of normal
• Forced vital capacity > 50% of normal
• DLCO normal
• Oxygen saturation > 92% on room air (for patients < 5 years of age)
• No history of allergic reactions attributed to compounds of similar chemical or biological composition to busulfan and fludarabine phosphate
• No ongoing or active infection
• No psychiatric illness or social situation that would preclude study compliance
• No other uncontrolled illness

PRIOR CONCURRENT THERAPY:

• See Disease Characteristics
• At least 4 weeks since prior and no concurrent surgery
• At least 4 weeks since prior and no other concurrent investigational or commercial agents or therapies for the malignancy, including chemotherapy, biologic therapy, or radiotherapy